Write equations of parabolas in vertex form from graphs

Learning Objectives Identify the vertex (h, k) of a parabola directly from its graph. Identify a second distinct point (x, y) on a parabola from its graph. Substitute the vertex and a second point into the vertex form of a parabola's equation. Algebraically solve for the 'a' value, which determines the parabola's stretch and direction. Write the final equation of a parabola in vertex form, y = a(x - h)² + k. Determine the sign of 'a' (positive or negative) by observing whether the parabola opens upwards or downwards. Ever wondered how the graceful arc of a basketball shot or a fountain's spray can be described with a simple equation? 🏀 Let's find out! This tutorial will guide you through the process of looking at a parabola's gr...

TermDefinitionExample ParabolaA U-shaped curve that is the graph of a quadratic function. Every point on the parabola is equidistant from a fixed point (the focus) and a fixed line (the directrix).The path of a ball thrown in the air follows a parabolic curve. VertexThe highest (maximum) or lowest (minimum) point on a parabola, also known as the turning point.In the graph of y = (x - 3)² + 4, the vertex is at the point (3, 4). Axis of SymmetryA vertical line that passes through the vertex and divides the parabola into two mirror-image halves.For a parabola with vertex (h, k), the axis of symmetry is the vertical line with the equation x = h. Vertex FormA standard way to write the equation of a parabola that clearly shows the vertex: y = a(x - h)² + k.The equation y = 2(x - 1)² - 5 is in v...

Vertex Form of a Parabola y = a(x - h)^2 + k This is the primary formula used to write the equation of a parabola that opens upwards or downwards. (h, k) represents the coordinates of the vertex, and 'a' determines the stretch, compression, and direction of opening. Formula to Isolate 'a' a = \frac{y - k}{(x - h)^2} To find the value of 'a', you can rearrange the vertex form. Substitute the coordinates of the vertex (h, k) and any other point (x, y) from the graph into this formula and solve.